Answer:
H0 : μ = 8
H1 : μ < 8
Test statistic = - 7.51
conclude that there is statistical significance that student at the school get less than 8 hours of sleep on average.
Step-by-step explanation:
The hypothesis :
H0 : μ = 8
H1 : μ < 8
The test statistic :
(xbar - μ) ÷ (s/√(n))
Sample data :
1.75, 2, 2.25, 2.25, 2.5, 3, 3.5, 3.5, 3.5, 3.75, 4, 4.25, 4.5, 4.5, 4.5, 4.75, 5.25, 5.5, 5.75, 5.75, 5.75, 6, 6, 6, 6.25, 6.25, 6.25, 6.5, 6.5, 6.5, 6.75, 7, 7, 7, 7.5, 7.5, 7.75, 8, 8.25, 8.25, 8.25, 8.5, 8.75, 9, 9
Using calculator :
Sample mean, xbar = 5.71666
Sample standard deviation, s = 2.04
The test statistic :
(5.7166 - 8) ÷ (2.04/√(45))
-2.28 / 0.3041052
= - 7.5085
= - 7.51
Degree of freedom = 45 - 1 = 44
Pvalue(-7.51, 44) = 0.00001
α = 1% = 0.01
Since Pvalue < α ; we reject H0 and conclude that there is statistical significance that student at the school get less than 8 hours of sleep on average.
Find all the roots of the given function on the given interval. Use pre-liminary analysis and graphing to find good initial approximations.
f(x) = cos (4x) - 4x2 + 9x
Answer:
The roots for [tex]f(x) = \cos 4x - 4\cdot x^{2} + 9\cdot x[/tex] are [tex]x_{1} = -0.098[/tex] and [tex]x_{2} = 2.166[/tex], respectively.
Step-by-step explanation:
A root is a value of [tex]x[/tex] so that [tex]f(x) = 0[/tex]. Let suppose that function is the consequence of the subtraction between two functions, that is:
[tex]f(x) = g(x) - h(x)[/tex] (1)
If we know that [tex]f(x) = 0[/tex], [tex]g(x) = \cos 4 x[/tex] and [tex]h(x) = 4\cdot x^{2}-9\cdot x[/tex], then we have the following identity:
[tex]g(x) = h(x)[/tex]
We can estimate graphically the roots of [tex]f(x)[/tex] by graphing the following system:
[tex]y = \cos 4x[/tex] (2)
[tex]y = 4\cdot x^{2}-9\cdot x[/tex] (3)
Where roots are the points in which functions find each other.
With the help of a graphing, we estimate two solutions:
[tex](x_{1}, y_{1}) = (-0.098, 0.924)[/tex], [tex](x_{2}, y_{2}) = (2.166, -0.725)[/tex]
What is the solution to 2x^2+8x=x^2-16?
x=4
x=-2
х=2
х=4
Question: What is the solution to 2x^2+8x=x^2-16?
Answer: x=-4 is what I got I'm not sure if u meant to put one of the 4's as -4 but yeah I got -4 and did it twice and got -4 again. Hope that helped.
Find the equation of a line that contains the points (0,0) and (6,−7). Write the equation in slope-intercept form, using fractions when required.
Use the slope formula below:
[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
To form an equation of a line - we need to find a slope and the y-intercept from y = mx+b. We are given two points which we can substitute in the formula.
[tex] \large{m = \frac{0 - ( - 7)}{0 - 6} } \\ \large{m = \frac{0 + 7}{ - 6} \longrightarrow \frac{7}{ - 6} } \\ \large \boxed{m = - \frac{7}{6} }[/tex]
We have finally got the slope. Next is to find the y-intercept. First we rewrite the equation of y = mx+b by substituting the slope.
[tex] \large \boxed{y = mx + b}[/tex]
The equation above is the slope-intercept form. Substitute m = -7/6 in the equation.
[tex] \large{y = - \frac{7}{6} x + b}[/tex]
Since the graph passes through (0,0) which is an origin point. In y = mx+b if the graph passes through origin point, that means the b-value is 0. Therefore:
[tex] \large \boxed{y = - \frac{7}{6} + 0 \longrightarrow y = - \frac{7}{6} x}[/tex]
Answer
y = -7x/6Hope this helps and let me know if you have any doubts! Good luck on your assignment!
Find the percent increase in volume when 1 foot is added to each dimension of the prism. Round your answer to the nearest tenth of a percent.
Percent increase ≈
%
Answer:
10
Step-by-step explanation:
WILL MARK BRAINLIEST
Answer:
25.12 cm
Step-by-step explanation:
circumference= 2pi*r
3.14x8x2= 50.24
50.24/2= 25.12 cm
Or you could have just done 3.14 x8 which equals 25.12 as well
SOMEONE HELP ME PLEASE
The XYZ Car Rental Agency charges a flat rate of $29 per day plus $0.32 per mile driven. Write an algebraic expression for the rental cost of a car for x days that is driven y miles.
Answer:
Total Cost = 29x + 0.32y
Step-by-step explanation:
It is 29x since you pay $29 per day, and x represents the number of days.
It is 0.32y since you pay $0.32 per mile, and y represents the number of miles.
The Sugar Sweet Company is going to transport its sugar to market. It will cost 4500 to rent trucks, and it will cost an additional 255 for each ton of sugar transported.
Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S Then use this equation to find the total cost to transport 16 tons of sugar.
Answer:
C(s) = total cost function
$5,500 base price to rent trucks
$250 per ton of sugar to be transported
Total Cost = Price per ton of sugar * # of tons + total cost to rent trucks
C(s) = $250s + $5,500
For 14 tons of sugar the total cost would be:
C(s) = $250(14 tons) + $5,500
C(s) = $9,000
Total cost to transport 14 tons of sugar would cost $9,000
Rewrite log(8)-log(2) in form log(c)
Answer:
log(4).
Step-by-step explanation:
By the law of logarithms:
log(8) - log(2)
= log(8/2)
= log(4).
Gopi paid 25% of his salary as tax and spent of his salary on groceries. The remaining amount of Rs.2500 was his savings. Find his salary and the tax amount paid.
Answer:
his salary is rs 6000 & his tax amount is rs 1500 :)
Answer:
6000,1500
Step-by-step explanation:
Let Gopi's salary be 'x'
He paid 25% of his salary as tax. = 25% of x = 25x/100 = x/4
He spent 1/3 of his salary on groceries = x/3
Getting his salary:-
x-x/3-x/4=2500
(12x-4x-3x)/12=2500
5x/12=2500
x=
(2500x12)/5
x=500x12=6000
Tax amount:-
6000x25/100=1500
Please give me the right answer me going onto my sophomore year depends on this
Answer: 5.5. if you divide you will clearly see it is 5.5 so D
Step-by-step explanation:
what is the answer to this question??
The radius of a circle is increasing at a rate of 6 centimeters per minute. Find the rate of change of the area when the radius is 4 centimeters.
Answer:
The rate of change is of of the area when the radius is 4 centimeters [tex]48\pi[/tex] square centimeters.
Step-by-step explanation:
Area of a circle:
The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
Implicit derivative:
To solve this question, we have to derivate implictly the equation as a function of t. Thus:
[tex]\frac{dA}{dt} = 2\pi r \frac{dr}{dt}[/tex]
The radius of a circle is increasing at a rate of 6 centimeters per minute.
This means that [tex]\frac{dr}{dt} = 6[/tex]
Find the rate of change of the area when the radius is 4 centimeters.
This is [tex]\frac{dA}{dt}[/tex] when [tex]r = 4[/tex]. Thus
[tex]\frac{dA}{dt} = 2\pi r \frac{dr}{dt} = 2\pi(4)(6) = 48\pi[/tex]
The rate of change is of of the area when the radius is 4 centimeters [tex]48\pi[/tex] square centimeters.
which will result in a perfect square trimonial
Answer:
No choices listed.
Step-by-step explanation:
Which inequality represents all numbers x on a number line that are farther from −8 than from −4?
Answer:
x - 8>-4-x
Step-by-step explanation:
Looking at x - 8>-4-x
Collect the like terms;
x+x > -4 + 8
2x < 4
x > 4/2
x < 2
Since the values of x are greater than 2,this shows that they are positive values and will be farther from -8 than -4
Given the logistic model f(x)= 800/1+19e^-0.402x
what is the initial value? Round your answer to the nearest whole number.
9514 1404 393
Answer:
40
Step-by-step explanation:
The "initial value" is the value when x=0.
[tex]f(x)=\dfrac{800}{1+19e^{-0.402x}}\\\\f(0) =\dfrac{800}{1+19e^0}=\dfrac{800}{1+19}=\dfrac{800}{20}\\\\=\boxed{40}[/tex]
The initial value is 40.
Kevin and his elder brother Jason jog every morning. Kevin runs 1.5 miles per hour slower
than Jason. When Jason ran 5 miles, Kevin only ran 4.2 miles. Find their running speeds.
(Write an algebraic equation first, then solve.)
Answer:
Jason - 9.375 miles per hour
Kevin -7.875 miles per hour
Step-by-step explanation:
Let Jason’s running speed be x miles per hour
Kevin runs 1.5 miles per hour less;
so his running speed will be (x-1.5) miles per hour
At any point, distance = speed * time
Their running time is same here;
Jason’s running time will be 5/x
Kevin’s running time will be 4.2/(x-1.5)
These times are equal;
So;
5/x = 4.2/(x-1.5)
5(x-1.5) = 4.2x
5x - 7.5 = 4.2x
5x-4.2x = 7.5
0.8x = 7.5
x = 7.5/0.8
x = 9.375 miles per hour
So kevin’s speed will be 9.375 - 1.5 = 7.875 miles per hour
write the next steps
Answer:
Two steps:
a) 12345×8+5=98765
b)123456×8+6=987654
answer to the question
Answer:
b. DC = 29 and DE = 44.5
Step-by-step explanation:
Given:
AB = 29
BD = 89
Required:
DC and DE
Solution:
✔️DC = AB (opposite sides of a parallelogram are equal)
Therefore,
DC = 29 (Substitution)
✔️DE = half of diagonal BD (Diagonals of a parallelogram bisect each other)
DE = ½(89)
DE = 44.5
Historically, the average diameter of the holes drilled has been 0.25 cm and the average range has been 0.10 cm. Samples of size 4 will be collected. For the R-chart, what is the value of upper control limit
Solution :
Given the average range of the holes drilled = 0.10 cm
The average diameter of the holes drilled = 0.25 cm
The sample size = 4
For the sample size of 4, the factor for control limit for the range ([tex]D_4[/tex]) = 2.28 (From the table of constants for X-bar and R-chart)
The upper control limit for the R-chart = R-bar x [tex]D_4[/tex]
= 0.10 x 2.28
= 0.228
Therefore, the answer is greater than 0.202 but less than or equal to 0.302
What is the value of n in the equation below?
Power with the same base
Resuelve el siguiente paralelo 27v r1 9r2 18 r37 r42
Charlene paid $1540.77 (including sales tax) for a microscope. The sales tax in her state is 7%.
What was the price of the microscope before the sales tax was added?
Answer:
1,439.97
Step-by-step explanation:
Price x 1.07 = price including sales tax
price x 1.07=1540.77
price=1540.77/1.07
price= 1439.97
The price of the microscope before the sales tax was added when calculated is; $1439.97
How to solve algebra problems?
We are told that Charlene paid $1540.77 (including sales tax) for a microscope. Thus, the price before sales tax can be gotten from the formula;
Price before sales tax × 1.07 = Price including sales tax
Thus, plugging in the relevant values;
Price before sales tax × 1.07 = 1540.77
Price before sales tax = 1540.77/1.07
Price before sales tax = $1439.97
Read more about Algebra Problems at; https://brainly.com/question/4344214
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Please help me I need to solve for x.
Find X so that a parallel to b
Step-by-step explanation:
4x+11+8x+1=180 (the two angles given is supplementary angles)
11x+12= 180
11x=168
x=168/11
x=15.27
please give brainly if it helps
Answer:
x = 14
Step-by-step explanation:
Same side interior angles are supplementary.
Therefore ,
( 4x + 11)° + ( 8x + 1 )° = 180 °
4x + 11 + 8x + 1 = 180
12x + 12 = 180
12x = 180 - 12
12x = 168
x = 14
Which equation represents the slope-intercept form of the line below?
y-intercept = (0,-6)
slope = -5
O A. y = -6x + 5
O B. y = -5x - 6
O C. y = -5x + 6
D. y = -6x-5
Hi there!
»»————- ★ ————-««
I believe your answer is:
Option B: [tex]y=-5x-6[/tex]
»»————- ★ ————-««
Here’s why:
Recall that the slope intercept form of a equation for a line is:⸻⸻⸻⸻
[tex]\boxed{\text{Slope-Intercept Form:}}\\\\------------\\y=mx+b\\\\\boxed{\text{\underline{Key}}}\\\\\rightarrow\text{m - slope}\\\\\rightarrow\text{b - y-intercept}[/tex]
⸻⸻⸻⸻
We are given the information of:
The slope, which is -5.The y-intercept, which is (0, -6).⸻⸻⸻⸻
[tex]\boxed{\text{Replace The Variables with The Appropriate Values:}}\\\\y=mx+b\\\\\rightarrow\text{-5 would replace 'm', -6 would replace 'b'.}\\\\\text{\underline{Therefore:}}\\\\y=mx+b\rightarrow\boxed{y=-5x-6}[/tex]
⸻⸻⸻⸻
Option B should be the correct answer.
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Find the maximum or minimum value of y = 3x² + 7x + 9 by completing the squares state the value of x at which the function is maximum or minimum.
Answer:
The minimum is 59/12
Step-by-step explanation:
you should calculate the -b/2a = -7/6
you should put -7/6 in the x variable
A basketball team recently scored a total of 94 points on a combination of 2-point field goals, 3-point field goals, and 1-point foul shots. Altogether, the team made 52 baskets and 11 more 2-pointers than foul shots. How many shots of each kind were made?
Answer:
The team converted 7 3-point shots, 28 2-point shots, and 17 foul shots.
Step-by-step explanation:
Since a basketball team recently scored a total of 94 points on a combination of 2-point field goals, 3-point field goals, and 1-point foul shots, and altogether, the team made 52 baskets and 11 more 2-pointers than foul shots, to determine how many shots of each kind were made, the following calculations must be performed:
19 x 3 + 22 x 2 + 11 x 1 = 57 + 44 + 11 = 112
9 x 3 + 27 x 2 + 16 x 1 = 27 + 54 + 16 = 97
7 x 3 + 28 x 2 + 17 x 1 = 21 + 56 + 17 = 94
Therefore, the team converted 7 3-point shots, 28 2-point shots, and 17 foul shots.
Find solution for 2(3^x)=5
Answer:
Step-by-step explanation:
i don’t know
Which points are on the graph of the function rule f(x) = 10 - 4x
Convert 240. oz = lb
Answer:
15
Step-by-step explanation:
If you want to convert Oz to lb then divide by 16
240/16
15
